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a(n) = binomial((n+1)*(2*n+1), n) / ((n+1)*(2*n+1)).
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%I #6 Feb 19 2018 12:39:13

%S 1,1,7,117,3311,135408,7324878,495729741,40411916335,3861208027677,

%T 423601805745460,52513639293534510,7263163165618323432,

%U 1109176062938132317300,185415009041446934481180,33681956588219177374026429,6607825171826115567872400495,1392510451119380284814728497375

%N a(n) = binomial((n+1)*(2*n+1), n) / ((n+1)*(2*n+1)).

%C a(n) = A299428(n) / (n+1)^2.

%H Paul D. Hanna, <a href="/A299429/b299429.txt">Table of n, a(n) for n = 0..200</a>

%o (PARI) {a(n) = binomial((n+1)*(2*n+1), n)/((n+1)*(2*n+1)) }

%o for(n=0,20,print1(a(n),", "))

%Y Cf. A299427, A299428.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Feb 19 2018